Name: _________________________________ Geometry Regents #3

1) William is drawing pictures of cross sections of the right circular cone below.

Which drawing can not be a cross section of a cone?

2) An equation of a line perpendicular to the line represented by the equation and

passing through is

1)

3)

2)

4)

3) In parallelogram QRST shown below, diagonal is drawn, U and V are points on and

, respectively, and intersects at W.

If , , and , what is ?

1) 37º 3) 72º

2) 60º 4) 83º

1)

3)

2)

4)

4) A fish tank in the shape of a rectangular prism has dimensions of 14 inches, 16 inches, and

10 inches. The tank contains 1680 cubic inches of water. What percent of the fish tank is

empty?

1) 10 3) 50

2) 25 4) 75

5) Which transformation would result in the perimeter of a triangle being different from the

perimeter of its image?

1) 3)

2) 4)

6) In the diagram below, bisects at B, and bisects at C.

Which statement is always true?

1) 3) bisects at C.

2) 4) bisects at B.

7) As shown in the diagram below, a regular pyramid has a square base whose side

measures 6 inches.

If the altitude of the pyramid measures 12 inches, its volume, in cubic inches, is

1) 72 3) 288

2) 144 4) 432

8) Triangle ABC and triangle DEF are graphed on the set of axes below.

Which sequence of transformations maps triangle ABC onto triangle DEF?

9) In , the complement of is . Which statement is always true?

1) 3) 2) 4)

10) A line that passes through the points whose coordinates are and is dilated by a

scale factor of 3 and centered at the origin. The image of the line

1) is perpendicular to the original line 3) passes through the origin

2) is parallel to the original line 4) is the original line

11) Quadrilateral ABCD is graphed on the set of axes below.

When ABCD is rotated 90° in a counterclockwise direction about the origin, its image is

quadrilateral A'B'C'D'. Is distance preserved under this rotation, and which coordinates

are correct for the given vertex?

1) no and 3) yes and

2) no and 4) yes and

1) a reflection over the x-axis followed

by a reflection over the y-axis

3) a 90° clockwise rotation about the

origin followed by a reflection over

the y-axis

2) a 180° rotation about the origin

followed by a reflection over the line

4) a translation 8 units to the right and 1

unit up followed by a 90°

counterclockwise rotation about the

origin

12) In the diagram below of circle O, the area of the shaded sector LOM is .

If the length of is 6 cm, what is ?

13) In the diagram below, .

If and , which statement will justify similarity by SAS?

1) , , and 3) , , and

2) , , and 4) , , and

14 The diameter of a basketball is approximately 9.5 inches and the diameter of a tennis ball

is approximately 2.5 inches. The volume of the basketball is about how many times

greater than the volume of the tennis ball?

1) 3591 3) 55

2) 65 4) 4

15 The endpoints of one side of a regular pentagon are and . What is the perimeter

of the pentagon?

1) 3) 2) 4)

1) 10º 3) 40º

2) 20º 4) 80º

16 In the diagram of right triangle ABC shown below, and .

What is the measure of , to the nearest degree?

1) 33 3) 50

2) 40 4) 57

17 What are the coordinates of the center and length of the radius of the circle whose

equation is ?

1) and 36 3) and 36

2) and 6 4) and 6

18 The coordinates of the vertices of are , , and . Which type of

triangle is ?

1) right 3) obtuse

2) acute 4) equiangular

19 Molly wishes to make a lawn ornament in the form of a solid sphere. The clay being used

to make the sphere weighs .075 pound per cubic inch. If the sphere's radius is 4 inches,

what is the weight of the sphere, to the nearest pound?

1) 34 3) 15

2) 20 4) 4

20 The ratio of similarity of to is . If and , then the

length of is

1) 5 3) 10

2) 7 4) 20

21 In the diagram below, , , , , and are chords of circle O, is tangent

at point D, and radius is drawn. Sam decides to apply this theorem to the diagram:

“An angle inscribed in a semi-circle is a right angle.”

Which angle is Sam referring to?

1) 3) 2) 4)

22 In the diagram below, is the altitude drawn to the hypotenuse of right

triangle ABC.

Which lengths would not produce an altitude that measures ?

1) and 3) and

2) and 4) and

23 A designer needs to create perfectly circular necklaces. The necklaces each need to have a

radius of 10 cm. What is the largest number of necklaces that can be made from 1000 cm

of wire?

1) 15 3) 31

2) 16 4) 32

24 In shown below, points T and O are on and , respectively. Segment OT is

drawn so that .

If , , and , what is the length of ?

1) 5.6 3) 11

2) 8.75 4) 15

25 Triangle ABC is graphed on the set of axes below. Graph and label

, the image of after a reflection over the line .

26 In the diagram below of circle O with diameter and radius , chord is

parallel to chord .

If , determine and state .

27 Directed line segment PT has endpoints whose coordinates are and .

Determine the coordinates of point J that divides the segment in the ratio 2 to 1. [The use

of the set of axes below is optional.]

28 As graphed on the set of axes below, is the image of after

a sequence of transformations.

Is congruent to ? Use the properties of rigid motion to

explain your answer.

29 A carpenter leans an extension ladder against a house to reach the bottom of a window 30

feet above the ground. As shown in the diagram below, the ladder makes a 70° angle with

the ground. To the nearest foot, determine and state the length of the ladder.

30 During an experiment, the same type of bacteria is grown

in two petri dishes. Petri dish A has a diameter of 51 mm

and has approximately 40,000 bacteria after 1 hour. Petri

dish B has a diameter of 75 mm and has approximately

72,000 bacteria after 1 hour.

Determine and state which petri dish has the greater

population density of bacteria at the end of the first hour.

31 Line is mapped onto line m by a dilation centered at the origin with a scale factor of 2.

The equation of line is . Determine and state an equation for line m.

32 The aspect ratio (the ratio of screen width to height) of a rectangular flat-screen television

is . The length of the diagonal of the screen is the television's screen size. Determine

and state, to the nearest inch, the screen size (diagonal) of this flat-screen television with a

screen height of 20.6 inches.

33 Given the theorem, “The sum of the measures of the interior angles of a triangle is 180°,”

complete the proof for this theorem.

Given:

Prove:

Fill in the missing reasons below.

34 Triangle XYZ is shown below. Using a compass and straightedge, on the line below,

construct and label , such that . [Leave all construction marks.]

Based on your construction, state the theorem that justifies why is congruent to

.

35 Given: Parallelogram ANDR with and bisecting and at points W and E,

respectively

Prove that . Prove that quadrilateral AWDE is a parallelogram.

36 Cathy wants to determine the height of the flagpole shown in the diagram below. She uses

a survey instrument to measure the angle of elevation to the top of the flagpole, and

determines it to be 34.9°. She walks 8 meters closer and determines the new measure of

the angle of elevation to be 52.8°. At each measurement, the survey instrument is 1.7

meters above the ground.

Determine and state, to the nearest tenth of a meter, the height of the flagpole.